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%I #5 Jul 16 2015 05:10:39
%S 1,0,0,1,0,0,2,0,0,3,1,0,4,2,2,5,3,4,9,5,6,13,11,10,19,17,19,28,27,31,
%T 44,41,49,66,68,74,98,104,118,145,157,178,220,234,268,322,354,397,473,
%U 521,591,686,765,863,1003,1107,1254,1444,1609
%N Shift sequence A162932 twice then subtract from the original sequence.
%C From _Alford Arnold_, Dec 17 2009: (Start)
%C at N=24, six of the partitions can be associated with the sixth row of this
%C triangular array:
%C 333
%C 444 3333
%C 555 4443 33333
%C 666 5553 44433 333333
%C 777 6663 55533 444333 3333333
%C 888 7773 66633 555333 4443333 33333333
%C The other three partitions are new; and hence on their first row, so 6*1+1*3=9
%C In a similar manner, the 44 cases at N=36 can be computed using the array row
%C numbers and the number of applicable partitions. Thus we have:
%C (10, 5, 3, 2, 1) times (1, 3, 2, 3, 7) providing 10+15+6+6+7 = 44 cases. (End)
%e For n= 24 the sequence counts these nine partitions: 888 7773 66633 55554 555333 4443333 6666 444444 33333333
%Y Cf. A000041 A002865 A053445 A162932
%K nonn
%O 6,7
%A _Alford Arnold_, Aug 05 2009, Aug 06 2009
%E More terms from _Alford Arnold_, Dec 17 2009
%E Added more terms, _Joerg Arndt_, Jul 16 2015
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